Simplify the following expression: $ z = \dfrac{-6p}{p + 3} - \dfrac{-7}{4} $
In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{4}{4}$ $ \dfrac{-6p}{p + 3} \times \dfrac{4}{4} = \dfrac{-24p}{4p + 12} $ Multiply the second expression by $\dfrac{p + 3}{p + 3}$ $ \dfrac{-7}{4} \times \dfrac{p + 3}{p + 3} = \dfrac{-7p - 21}{4p + 12} $ Therefore $ z = \dfrac{-24p}{4p + 12} - \dfrac{-7p - 21}{4p + 12} $ Now the expressions have the same denominator we can simply subtract the numerators: $z = \dfrac{-24p - (-7p - 21) }{4p + 12} $ Distribute the negative sign: $z = \dfrac{-24p + 7p + 21}{4p + 12}$ $z = \dfrac{-17p + 21}{4p + 12}$